Beat butter with electric mixer until creamy. Gradually add the maple syrup, mixing until well combined. Can be prepared up to 1 week in advance.

Whisk together eggnog with egg, vanilla extra and cinnamon in a medium bowl. Dunk the bread in the eggnog mixture for 15 seconds, making sure the bread fully absorbs the liquid.

Heat 1 tbsp maple butter on a griddle or nonstick pan over medium heat. Place the prepared challah on the pan and cook until golden brown, about 4-5 minutes. Flip and cook on the other side until golden brown, another 3-4 minutes. Remove from heat and keep warm.

Melt 2 tbsp maple butter in the same pan over medium-high heat. Add the bananas and sugar and toss to coat. Remove the skillet from heat and pour the rum. Return to heat and cook until the sugar has dissolved, about 1 minute. Add cinnamon and nutmeg and stir to coat. Remove from heat.